The diameter of a circle is 12 inches. What is the length of a 90° arc?

Question

 The diameter of a circle is 12 inches. What is the length of a 90° arc?

 

 

Answer 1

1.  calculate the circumference, 2(pi)r

2. divide by four because 90 degrees is one fourth of the whole circle

Answer 2

Note the definition of:  Π = C/d     [circumference of circle divided by diameter]

     So, C=Πd

 

A 90° arc is 1/4 of the 360° circle (that is, of the entire circumference)

 

If the diameter is 12, the 90° arc is (1/4)Π(12), or 3Π  (approximately 9.42).